Suppose the speed of sound is $c$ feet per second, and gravity is $g$ feet per second squared. If you drop the rock at time $x=0$ seconds then after $x$ seconds the rock will fall $$d(x) = \frac{1}{2}gx^2$$ feet. Suppose you hear the impact after $t$ seconds. Then the depth of this well is
$d=$ .
(Your answer will be a mathematical expression involving $t$, $g$, and $c$.)
Set up and solve a quadratic equation.